Generally speaking, the HOEVD solution is not a critical point to the symmetric tensor cost REF  [1]}.
Its approximation error to a \(d\) -th order tensor \({X}\)  is estimated by [2]} as
\(\left\Vert {X}- \hat{{X}}_{\text{hoevd}} \right\Vert  \le \sqrt{d}\left\Vert {X}- \hat{{X}}_{\text{best}} \right\Vert .\) 
